Interfaces, strings, and a soft mode in the square lattice quantum dimer model

The quantum dimer model on the square lattice is a U(1) gauge theory that addresses aspects of the physics of high-Tc superconductors. Using a quantum Monte Carlo method, we show that the theory exists in a confining columnar valence bond solid phase. The interfaces separating distinct columnar phases display plaquette order, which, however, is not realized as a bulk phase. Static “electric” charges are confined by flux tubes that consist of multiple strands, each carrying a fractionalized flux ¼. A soft pseudo-Goldstone mode (which becomes exactly massless at the Rokhsar-Kivelson point) extends deep into the columnar phase, with potential implications for high-Tc physics.

Fourier Series by Least Square Minimization

An introduction to Fourier Series based on the minimization of the least square error between an approximate series representation and the exact function.

Statue de Berlioz du Square Bintmille, à Paris et à La Cote-Saint-André

Signatur des Originals: S 36/F03013

Decomposition of $\rm R\times C$ contingency table chi -square: Application to binned DNA fragment size data and population structure analysis

The purpose of this research is to develop a new statistical method to determine the minimum set of rows (R) in a R x C contingency table of discrete data that explains the dependence of observations. The statistical power of the method will be empirically determined by computer simulation to judge its efficiency over the presently existing methods. The method will be applied to data on DNA fragment length variation at six VNTR loci in over 72 populations from five major racial groups of human (total sample size is over 15,000 individuals; each sample having at least 50 individuals). DNA fragment lengths grouped in bins will form the basis of studying inter-population DNA variation within the racial groups are significant, will provide a rigorous re-binning procedure for forensic computation of DNA profile frequencies that takes into account intra-racial DNA variation among populations. ^

Knowledge Creation as a Square Dance on the Hilbert Cube

This paper presents a micro-model of knowledge creation and transfer in a small group of people. Our model incorporates two key aspects of the cooperative process of knowledge creation: (i) heterogeneity of people in their state of knowledge is essential for successful cooperation in the joint creation of new ideas, while (ii) the very process of cooperative knowledge creation a¤ects the heterogeneity of people through the accumulation of knowledge in common. The model features myopic agents in a pure externality model of interaction. In the two person case, we show that the equilibrium process tends to result in the accumulation of too much knowledge in common compared to the most productive state. Unlike the two-person case, in the four person case we show that the equilibrium process of knowledge creation may converge to the most productive state. Equilibrium paths are found analytically, and they are a discontinuous function of initial heterogeneity.

‘This square is our home!’: the organisation of urban space in the spanish 15M movement

Why should a progressive planner/urbanist pay attention to the Spanish 15M movement? From a disciplinary standpoint, its most complex and interesting aspect, which could hypothetically be transferred to other contexts (as in fact happened in the Occupy Wall Street and Occupy London movements), is its 'spatiality'. This article analyses the spatial practices of the so called #spanishrevolution, one of the 2011 social movements that showed the possibility for a new collective appropriation and self-management (autogestion) of urban public space. Although the political goals of the movement were vague at the time of its inception, the practices and spatial imaginaries deployed by it have become consolidated and proven to be yet another of its more successful facets in promoting the spreading and organisation of the protest, making it a phenomenon that calls for reflection on the part of urban thinkers and planners.

Classification of discrete systems on a square lattice

We consider the classification up to a Möbius transformation of real linearizable and integrable partial difference equations with dispersion defined on a square lattice by the multiscale reduction around their harmonic solution. We show that the A1, A2, and A3 linearizability and integrability conditions constrain the number of parameters in the equation, but these conditions are insufficient for a complete characterization of the subclass of multilinear equations on a square lattice.

Benchmarking of calculation schemes in Apollo2 and COBAYA3 for VVER lattices

This paper presents solutions of the NURISP VVER lattice benchmark using APOLLO2, TRIPOLI4 and COBAYA3 pin-by-pin. The main objective is to validate MOC based calculation schemes for pin-by-pin cross-section generation with APOLLO2 against TRIPOLI4 reference results. A specific objective is to test the APOLLO2 generated cross-sections and interface discontinuity factors in COBAYA3 pin-by-pin calculations with unstructured mesh. The VVER-1000 core consists of large hexagonal assemblies with 2mm inter-assembly water gaps which require the use of unstructured meshes in the pin-by-pin core simulators. The considered 2D benchmark problems include 19-pin clusters, fuel assemblies and 7-assembly clusters. APOLLO2 calculation schemes with the step characteristic method (MOC) and the higher-order Linear Surface MOC have been tested. The comparison of APOLLO2 vs.TRIPOLI4 results shows a very close agreement. The 3D lattice solver in COBAYA3 uses transport corrected multi-group diffusion approximation with interface discontinuity factors of GET or Black Box Homogenization type. The COBAYA3 pin-by-pin results in 2, 4 and 8 energy groups are close to the reference solutions when using side-dependent interface discontinuity factors.